1. Field of the Invention
This invention relates to a detector of quantity of electricity for detecting a value of amplitude of quantity of electricity of AC voltage, AC current and the like, particularly to improvement of frequency characteristics thereof.
2. Description of Related Art
FIG. 1 is a figure explaining a principle of a conventional digital processing apparatus of a quantity of AC electricity disclosed in Japanese Patent Application No. 62-333434, the value of amplitude being determined by using three data which have been sampled with electrical angle 90.degree. of AC current being sampling cycle T. In the figure, assuming that a sampling value 1 of an appropriate time is i(O), a sampling value 2 preceding one cycle (T) being i(T), a sampling value 3 preceding two cycles (2T) being i(2T), sampling values 1.about.3 are squared, by square operating means 5.about.7 respectively, and only the result of the square operating means 6 is doubled by a double operating means 29.
The results obtained at aforesaid square operating means 5 and 7 are added to the result of aforesaid double operating means 29 by an adder means 11 so as to obtain the sum. The sum is divided by 2 by a divide operating means 30 and the square root is calculated by a square root operating means 13 to obtain, at a terminal 14, the output Fn thereof, being the value of amplitude of AC current.
Next, explanation will be given on the operation. For the convenience sake of the explanation, the quantity of AC electricity is assumed to be AC current, maximum value I, instantaneous magnitude i, fundamental blade frequency fo, and the sampling cycle T whose cycle is made to be 1/4 of the fundamental blade frequency fo. And in order to distinguish data at a sampling time, assuming that nT (where n =0, 1, 2, . . . , and n=0 being this time) is suffix, the sampling value of the appropriate time are expressed to be i(O), the sampling value preceding one cycle from the appropriate time to be i(T), and the sampling value preceding two cycles from the appropriate time to be i(2T). . . respectively.
When output Fn is expressed in any formula, the following first formula is obtained. ##EQU1##
The sampling cycle T is fixed to 1/4 cycle relative to where the fundamental frequency of the AC current, that is, a time period which corresponds to electrical angle 90.degree., however, where the frequency of the sampling time is f, the sampling cycle T is expressed as in the second formula. ##EQU2##
For example, the frequency of the AC current is f=fo =50 Hz, the sampling cycle T=90.degree. is established.
Generally, as an electric power system is operated by rated frequency fo, in formula (1), Fn=I is obtained, thereby the amplitude value of the current can be calculated, which, for example, is used for such as an AC excess current protection relay and a control apparatus. But, for the protection relay for detecting accidents being happened in the electric power system and for the control apparatus for detecting the quantity of electricity for controlling an operation apparatus, there are many cases where the frequency of the electric power system has changed from fo. But, even if there is some dislocation of frequency of the electric power system, there is a need to determine the value of amplitude accurately. Generally, in order to cope with the change of .+-.5% of the frequency, it is necessary to lessen errors as much as possible.
Now, assuming that the frequency f=52.5 Hz (increase of 5% of 50 Hz), formula T=94.5.degree. is obtained. When it is substituted in formula (1), the following formula is established: EQU Fn=I{1-0.0062cos(2.theta.-189.degree.)}.sup.1/2 ( 3).
Such result is obtained as that the constant value is degenerated by the amplitude waveform of double cycle. Since cos(2.theta.-189.degree.) can be changed from +1.0 to -1.0, the formula (3) becomes as EQU Fn=0.997I.about.1.003I (4),
thereby, the error of -0.3% to 0.3% is created compared with that of the operation of the amplitude value at the time when the rated frequency is 50 Hz.
Because the conventional detector of quantity of electricity is so constructed as above, there is a problem that the calculation of error of amplitude value is relatively larger in the case where the frequency varies to the extent of about .+-.5%.